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Systematic weakly nonlinear analysis of radial viscous fingering
E Alvarez-Lacalle1, E Pauné, J Casademunt
1Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain.
Summary
We analyzed interface dynamics in rotating and injecting Hele-Shaw cells. Nonlinear effects were found to increase instability, especially with lower viscosity contrast in centrifugal forcing scenarios.
Area of Science:
- Fluid dynamics
- Nonlinear analysis
- Hele-Shaw flow
Background:
- Hele-Shaw cells are crucial for studying fluid interfaces.
- Previous studies often focused on channel geometry or linear approximations.
- Understanding nonlinear effects is key for complex flow behaviors.
Purpose of the Study:
- To perform a weakly nonlinear analysis of interface dynamics in a radial Hele-Shaw cell.
- To investigate the combined effects of injection and rotation on fluid interfaces.
- To determine conditions for the uniform convergence of nonlinear expansions.
Main Methods:
- Extension of a systematic expansion method to radial geometry.
- Explicit computation of first nonlinear contributions.
- Comparison of analytical predictions with exact solutions and numerical integration.
Main Results:
- A condition for uniform convergence of the nonlinear expansion was identified.
- Analytical predictions showed good agreement with numerical and exact solutions.
- In purely centrifugal forcing, nonlinear couplings enhance interface instability with lower viscosity contrast.
Conclusions:
- The study provides a robust analytical framework for nonlinear interface dynamics in radial Hele-Shaw cells.
- The interplay of injection and rotation can maintain stable interface evolution.
- Nonlinear effects significantly influence interfacial stability, particularly in centrifugal flows.